Bayesian network structure learning using quantum generative models

Bryan O’Gorman, Ryan Babbush, Alejandro Perdomo‐Ortiz +2 more

Vicente P. Soloviev, Concha Bielza, Pedro Larrañaga

Enrico Zardini, Massimo Rizzoli, Sebastiano Dissegna +2 more

Bayesian networks are widely used probabilistic graphical models, whose structure is hard to learn starting from the generated data. O'Gorman et al. have proposed an algorithm to encode this task, i.e., the Bayesian network structure learning (BNSL), into a form that can be solved through quantum annealing, but they have not provided an experimental evaluation of it. In this paper, we present (i) an implementation in Python of O'Gorman's algorithm, (ii) a divide et impera approach that allows addressing BNSL problems of larger sizes in order to overcome the limitations imposed by the current architectures, and (iii) their empirical evaluation. Specifically, several problems with an increasing number of variables have been used in the experiments. The results have shown the effectiveness of O'Gorman's formulation for BNSL instances of small sizes, and the superiority of the divide et impera approach on the direct execution of O'Gorman's algorithm.

Radhakrishnan Balu, Ajinkya Borle

We report a scalable hybrid quantum-classical machine learning framework to build Bayesian networks (BN) that captures the conditional dependence and causal relationships of random variables. The generation of a BN consists of finding a directed acyclic graph (DAG) and the associated joint probability distribution of the nodes consistent with a given dataset. This is a combinatorial problem of structural learning of the underlying graph, starting from a single node and building one arc at a time, that fits a given ensemble using maximum likelihood estimators (MLE). It is cast as an optimization problem that consists of a scoring step performed on a classical computer, penalties for acyclicity and number of parents allowed constraints, and a search step implemented using a quantum annealer. We have assumed uniform priors in deriving the Bayesian network that can be relaxed by formulating the problem as an estimation Dirichlet parameters. We demonstrate the utility of the framework by applying to the problem of elucidating the gene regulatory network for the MAPK/Raf pathway in human T-cells using proteomics data where the concentration of proteins, nodes of the BN, are interpreted as probabilities.

Jincheng Zhang

This paper investigates the application of quantum-inspired optimization techniques to the problem of inference and learning within large-scale Bayesian Networks (BNs). Traditional Bayesian Network learning and inference methods often struggle with scalability, particularly as the number of nodes and dependencies increases. We propose leveraging concepts from quantum algorithms, specifically drawing inspiration from quantum annealing and quantum Monte Carlo methods, to efficiently explore the complex search space associated with BN structure optimization and parameter estimation. The core idea is to mimic the exploration capabilities of quantum systems to accelerate the process. The proposed methodology aims to improve the efficiency of BN learning and inference, potentially unlocking new capabilities for probabilistic reasoning in complex systems. This work presents a theoretical framework and a conceptual outline for such an approach, laying the groundwork for future research and experimentation. The effectiveness of this approach is predicated on the ability to translate the inherent parallelism of quantum algorithms into an efficient optimization strategy for Bayesian Networks.

Hiroshi Ohno